IMlM'.RFKCriONS 1M)1 CI.I) I\ SOLIDS BY FAS T-PARTICI.K IRRADIA'IK)\ 



In the case of irradiation by heavy particles or neutrons, one would not 

 ex])ect the displacements to be evenly distributed in space. While a charged 

 particle or a displaced atom has energy in excess of E, and loses energy by 

 electronic excitation, it moves some distance through the crystal, but it 

 creates most of its displacements when its energy has fallen below E^, that 

 is at the end of its range, when the particle and its progeny have a short 

 mean free path. Most of the displacements, therefore, occur in small 

 volumes at the end of the range or where energetic primary displacements 

 occurred, though there are also some isolated displacements, mainly early 

 displacements just above the threshold energy E^^. Thus there should be 

 displacement clusters, each containing say 50 to 100 displacements in a small 

 region, superimposed on a background of isolated displacements. Evidence 

 for this arrangement of displacements was obtained from low-temperature 

 thermal conductivity measurements by Herman, Simon, Klemens and Fry^, 

 to be discussed under the heading 'Thermal Conductivity' (p. 278). 



We must also consider the heat liberated by processes which do not cause 

 displacements. If sufficient heat is liberated in a small region, there will be 

 local melting, followed by solidification after the heat has been conducted 

 away. While displacements give rise to vacancies and interstitials only, or 

 their aggregates, melting and solidification may produce more complex 

 imperfections, such as dislocations. To determine the extent of the molten 

 region and its rate of cooling, the macroscopic equations of heat conduction 

 are sometimes used ; however, this procedure is valid only if the character- 

 istic dimensions are larger than the mean free path of the microscopic carriers 

 of heat (electrons in metals, lattice waves in insulators). 



It was pointed out by Seitz^ that the electronic excitation energy liberated 

 by a fast particle in the early part of its range will produce a heated region 

 of cylindrical shape, the 'thermal spike'. In the case of metals, the energy 

 given to the electrons will be distributed among all electrons in a given 

 region almost instantaneously, raising their temperature, while the lattice 

 temperature will initially lag behind. The hot electrons will move outwards 

 a distance /, their mean free path for interacting with lattice waves; the 

 time required to move this distance is also the time required to establish 

 thermal equilibrium with the lattice (typically of the order of 10~^^ sec). 

 After this time, the energy has been shared with the lattice and is distributed 

 throughout a cylindrical region of radius /, so that the average energy 

 increase of an atom in that region is : 



&' 



d^ TTi^n 



where n is the number of atoms per unit volume, and d£'/d^ is the_energy 

 loss of the fast particle per unit path length. It is the magnitude o^ E which 

 determines whether there is any melting; the subsequent outward flow of 

 heat may be described, \vithout serious error, in terms of macroscopic 

 conduction theory. 



In the case of copper (/~ 4x 10" cm), bombarded by 1 MeV electrons 

 (d£/d^~ lO^eV/cm) or by 1 MeV protons {dEjdz^ lO^eV/cm), E is only 

 2-5x10-^ and 2-5xlO-*eV respectively, leading to quite insignificant 

 temperature changes (1 degree ~ 10~'*eV). In materials of shorter electron 



274 



